ADC and DAC are well known. ADC and DAC are converters having a nonlinear transfer characteristic that produce harmonics, intermodulation and other nonlinear distortion components in the output signal. This nonlinear distortion can be compensated by a pre-processing of the digital input signal xD supplied to the DAC or by a post-processing of the digital output signal yD generated by the ADC.
K. Hariharan compensated static errors of an ADC by using a simple polynomial approach and an optimal estimation of parameters in the publication “A Method for ADC Error Testing and its Compensation in Ratiometric Measurements”, Measurement Science Review, Volume 10, no. 2, 2010.
J. Eklund corrected also static errors in the output signal of an ADC in U.S. Pat. No. 6,229,467 by comparing a measured histogram with an expected histogram. H. Hekstra used an iterative method in U.S. Pat. No. 8,410,960 to reduce the spectral flatness in the corrected output signal of the ADC. L. Pellon described in U.S. Pat. No. 6,271,781 a dynamic error calibration, which requires a high-quality generator. A. Bugeja revealed in U.S. Pat. No. 6,445,319 a compensation technique that captures exclusively static nonlinearities in the transfer function between an instantaneous analog input value Vin and an digital output value Vout. A. Glibbery describes a method for detecting static bit errors of an ADC in U.S. Pat. No. 7,129,879.
D. Hummel developed a dynamic compensation method in “Performance Improvement of All-digital Wide Bandwidth Receiver by Linearization of ADC and DAC”, Measurement 31 (2002), 35-45 Elsevier, to improve the spurious-free dynamic range (SFDR), that describes the difference in dB between the amplitude of a sine-wave test signal and the largest amplitude nonlinear distortion components in the analog output signal. This approach is limited to distortions, which are generated by the slew rate in the sample and hold circuitry of the ADC.
Y. Yang, identified in “Linearization of ADC via Digital Post Processing’, in proceeding of ISCAS May 15-19, Rio de Janeiro, 2011, pp. 989-992, the n-dimensional transfer function of a Volterra model by using a Vandermonde matrix and the frequency-selection method of S. Boyd, et. all. in “Measuring Volterra Kernels,” IEEE Trans. Circuits systems, vol. 30 No. 8, pp. 571-577, August 1983.
K. Shi used a Volterra approach for modeling of nonlinear transfer behavior of AD converter in “Blind Volterra system Linearization with Applications to Post Compensation of ADC Nonlinearities” in 2012 IEEE, ICASSP, S. 3581-3584. This procedure requires that the signal is band-limited, and there is a free spectral range for the analysis of the distortion generated by the ADC.